We are continuing our studies of the folding properties of single-domain proteins using simple statistical-mechanical models. In these models it is assumed that the folding properties of a protein are determined entirely by the intramolecular interactions present in its native folded conformation. Proteins are represented as chains of monomer units (corresponding to amino acid residues) each of which has only two possible conformational states, the "native" state, corresponding to the conformation assumed by the unit in the native structure of the chain, and the "random-coil" state, which encompasses all non-native conformations. The structural states of a polypeptide chain are then defined by the sequence of native/random-coil states of these monomers. The stability of any such state of the chain is determined by the offsetting effects of the destabilizing entropy losses associated with fixing monomers in the native conformation, and the stabilizing native non-bonding contacts between different parts of the chain. The map of native contacts is derived from the X-ray crystallographic or NMR-derived structure of the corresponding protein. In the simplest picture, a state with a specified sequence of native/random-coil monomers may only form those native contacts that connect parts of the chain lying in the same contiguous stretch of native monomers. In a more complete picture, contacts are also possible between parts of the chain separated by intervening stretches of non-native monomers and induce an additional destabilizing entropy loss by constraining the ends of the loops of random-coil chain formed by these non-native stretches. For specified values for the entropy losses of fixing a single unit in the native conformation and of closing loops of non-native chain, and for the energy of the intra-chain contacts, it is possible to enumerate the possible sequences of monomer native/random-coil states and their corresponding stabilities and thereby compute a model partition function of the chain. The intractably large number of states that arises from complete enumeration of the possible combinations of monomer states for typical chain lengths has motivated the calculation of partition functions in the so-called "single-sequence", "double-sequence", and "triple-sequence" approximations, in which only states which have at most one, two, or three contiguous stretches of native monomers, respectively, are included. These partition functions are used to compute the free energy for a given chain as a function of a single reaction coordinate defined for each state as either the total number of native monomers or the fraction of native contacts formed in that state; this "reaction free-energy surface" provides the basis for modeling the equilibrium and kinetic folding properties of the chain. In work reported in previous years, we used a "combinatorial modeling" procedure within this framework to identify which among a wide variety of possible model assumptions and features consistently produce the most accurate descriptions of the measured folding properties of a set of two-state proteins. More recently, we have been using the best-performing of these models to directly analyze an extensive set of equilibrium and kinetic measurements performed in our own laboratory of the folding of the single alpha-helical protein villin. Among the measurements being modeled is the equilibrium temperature dependence of the UV circular dichroism, which reflects the extent of alpha-helix formation concomitant with the folding process; in our model the helical content of each state of the protein chain is simply the combined lengths of contiguous stretches of native monomers in parts of the sequence that are helical in the native state. We also analyze both the equilibrium temperature dependence and the T-jump kinetics of the UV fluorescence, which probes the formation of locally compact protein structures through the degree of quenching of the fluorescence of the single tryptophan sidechain by contact with residues elsewhere in the chain; model states in which the fluorescence is quenched are precisely those in which a native contact between the tryptophan and the quenching residue(s) is formed. Preliminary results indicate that our simple model picture for the enumeration and stabilities of the various states of the protein chain, combined with a straightforward prescription for computing the spectroscopic properties of the individual states, describes quite well the equilibrium and kinetic spectroscopic measurements of the folding properties of this protein. In keeping with our interest in developing and exploiting new methods for probing the structural dynamics of macromolecules, we are collaborating with Philip Anfinrud's group in the Laboratory of Chemical Physics in the development of new algorithms for the analysis of Laue (i.e., polychromatic illumination) diffraction data acquired in time-resolved X-ray crystallographic studies of proteins. These algorithms include efficient procedures for the assignment of Miller indices to observed reflections, the integration of intensities to produce structure factors for these reflections, and the scaling of the resulting sets of structure factors from multiple images onto a common intensity scale. We have also created a fundamentally new prescription for extracting more accurate structure-factor information from the distributions of pixel intensities within the individual spots in a Laue diffraction image, based on a model description of the distribution of mosaic structures actually present in the crystal.